same binary precision. (However, the output value is
     currently never <emphasis>exactly</emphasis> midway between two
     representable values, in order to avoid a widespread bug where input
     routines do not properly respect the round-to-nearest-even rule.) This value will
     use at most 17 significant decimal digits for <type>float8</type>
     values, and at most 9 digits for <type>float4</type> values.
    </para>

    <note>
     <para>
      This shortest-precise output format is much faster to generate than the
      historical rounded format.
     </para>
    </note>

    <para>
     For compatibility with output generated by older versions
     of <productname>PostgreSQL</productname>, and to allow the output
     precision to be reduced, the <xref linkend="guc-extra-float-digits"/>
     parameter can be used to select rounded decimal output instead. Setting a
     value of 0 restores the previous default of rounding the value to 6
     (for <type>float4</type>) or 15 (for <type>float8</type>)
     significant decimal digits. Setting a negative value reduces the number
     of digits further; for example -2 would round output to 4 or 13 digits
     respectively.
    </para>

    <para>
     Any value of <xref linkend="guc-extra-float-digits"/> greater than 0
     selects the shortest-precise format.
    </para>

    <note>
     <para>
      Applications that wanted precise values have historically had to set
      <xref linkend="guc-extra-float-digits"/> to 3 to obtain them. For
      maximum compatibility between versions, they should continue to do so.
     </para>
    </note>

    <indexterm>
     <primary>infinity</primary>
     <secondary>floating point</secondary>
    </indexterm>

    <indexterm>
     <primary>not a number</primary>
     <secondary>floating point</secondary>
    </indexterm>

    <para>
     In addition to ordinary numeric values, the floating-point types
     have several special values:
<literallayout>
<literal>Infinity</literal>
<literal>-Infinity</literal>
<literal>NaN</literal>
</literallayout>
     These represent the IEEE 754 special values
     <quote>infinity</quote>, <quote>negative infinity</quote>, and
     <quote>not-a-number</quote>, respectively. When writing these values
     as constants in an SQL command, you must put quotes around them,
     for example <literal>UPDATE table SET x = '-Infinity'</literal>.  On input,
     these strings are recognized in a case-insensitive manner.
     The infinity values can alternatively be spelled <literal>inf</literal>
     and <literal>-inf</literal>.
    </para>

    <note>
     <para>
      IEEE 754 specifies that <literal>NaN</literal> should not compare equal
      to any other floating-point value (including <literal>NaN</literal>).
      In order to allow floating-point values to be sorted and used
      in tree-based indexes, <productname>PostgreSQL</productname> treats
      <literal>NaN</literal> values as equal, and greater than all
      non-<literal>NaN</literal> values.
     </para>
    </note>

    <para>
     <productname>PostgreSQL</productname> also supports the SQL-standard
     notations <type>float</type> and
     <type>float(<replaceable>p</replaceable>)</type> for specifying
     inexact numeric types.  Here, <replaceable>p</replaceable> specifies
     the minimum acceptable precision in <emphasis>binary</emphasis> digits.
     <productname>PostgreSQL</productname> accepts
     <type>float(1)</type> to <type>float(24)</type> as selecting the
     <type>real</type> type, while
     <type>float(25)</type> to <type>float(53)</type> select
     <type>double precision</type>.  Values of <replaceable>p</replaceable>
     outside the allowed range draw an error.
     <type>float</type> with no precision specified is taken to mean
     <type>double precision</type>.
    </para>

   </sect2>

   <sect2 id="datatype-serial">
    <title>Serial Types</title>

    <indexterm zone="datatype-serial">
     <primary>smallserial</primary>